Question

Two parallel plate capacitors $\text{A}$ and $\text{B}$ have capacitors $1\mu \text{F}$ and $5\mu \text{F}$ are charged separately to same potential of $100\text{V}$. Now the positive plate of $\text{A}$ is connected to the negative plate of $\text{B}$ and the negative plate of $\text{A}$ to the positive plate of $\text{A}$ then the loss of energy in this process is

• A. $1.37\times {10}^{-2}\text{J}$
• B. $1.67\times {10}^{-2}\text{J}$
• C. $2.25\times {10}^{-2}\text{J}$
• D. $2.75\times {10}^{-2}\text{J}$

Answer 1

The correct option is B $1.67\times {10}^{-2}\text{J}$

Loss in energy $\Delta U$ is,

$\Delta U=\frac{1}{2}\frac{C_1{C}_2}{C_1+C_2}(V_1+V_2{)}^2$

$=\frac{1}{2}\frac{1\times {10}^{-6}\times 5\times {10}^{-6}}{6\times {10}^{-6}}[100+100{]}^2$

$=\frac{5\times {10}^{-6}\times 4\times {10}^4}{12}$

$=\frac{20}{12}\times {10}^{-2}=\frac{5}{3}\times {10}^{-2}=1.67\times {10}^{-2}\text{J}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, (b) is the correct answer.